Problem

List every feasible ordered pair for \(x~+~y~\le~4\) when \(x\) and \(y\) are nonnegative whole numbers.

Big Picture

What this problem is really about

The solution set is discrete because both variables must be nonnegative whole numbers. We’ll take each possible x-value in order, use the sum constraint to determine the allowed y-values for that row, and record the resulting lattice points systematically. Including zero and the equality boundary ensures that no valid pairs are skipped.

Answer choices

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(1,0), (1,1), (1,2), (1,3), (2,0), (2,1), (2,2), (3,0), (3,1), (4,0)

(0,0), (0,1), (0,2), (0,3), (1,0), (1,1), (1,2), (2,0), (2,1), (2,2), (3,0), (3,1), (4,0)

(0,0), (0,1), (0,2), (0,3), (0,4), (1,0), (1,1), (1,2), (1,3), (2,0), (2,1), (2,2), (3,0), (3,1), (4,0)

(0,0), (0,1), (0,2), (0,3), (0,4), (1,0), (1,1), (1,2), (1,3), (2,0), (2,1), (2,2), (2,3), (3,0), (3,1), (4,0)

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List every feasible ordered pair for \(x~+~y~\le~4\) when \(x\) and \(y\) are nonnegative whole numbers.

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